Question

A particle starts moving with initial velocity 12 m/s according to the following acceleration-time graph. a (ms 5 8 0 t(s) -10 The velocity of particle at t = 2 s is 0 32 m/s 0 34 m/s 38 m/s 35 m/s​

Answer 1

A particle starts moving with initial velocity 12 m/s according to the following acceleration-time graph. a (ms 5 8 0 t(s) -10 The velocity of particle at t = 2 s is 0 32 m/s 0 34 m/s 38 m/s 35 m/s

Answer 2

A particle starts moving with initial velocity 12 m/s according to the following acceleration-time graph. [ The graph has been mentioned at the bottom of the answer]

The velocity of the particle at t = 2 s , is 32 m/s. so option (1) is correct.

acceleration-time graph :

• in this graph, area inclosed by the graph with the time axis gives the average velocity of the particle.
• to find the velocity of the particle at a particular time, observe the acceleration at that time, is it constant ? if yes , apply fundamental equations of kinematics. ( e.g., v = u + at , v² - u² + 2as etc.. )
• if acceleration at a particular time isn't constant then we have to use calculus (differentiation, integration etc..zz0  to find out unknown data.

we see in the graph,

acceleration upto 2 sec, is 10 m/s² and between 2 and 8 sec, is - 10 m/s².

so, acceleration of the particle, a = 10 m/s² [ at t = 2sec ]

initial velocity of the particle, u = 12 m/s

using formula, v = u + at

⇒ v = 12 + 10 × 2

⇒ v = 12 + 20

⇒ v = 32 m/s

Therefore the velocity of the particle at t = 2 sec, is 32m/s . hence option (1) 32 m/s , is correct.